IJAM, Volume 28, No. 3 (2015)

Abstract. One step hybrid numerical scheme for the direct solution of general second order ordinary differential equations is proposed in this paper. The scheme is developed using the collocation and interpolation techniques on the power series approximate solution and augmented by the introduction of one offstep point in order to circumvent Dahlquist zero stability barrier and upgrade the order of consistency of the method. The continuous implicit hybrid one step scheme obtained has the advantage of easy change of step length and evaluation of functions at offstep points. The block method used to implement the main method guarantees that each discrete method obtained from the simultaneous solution of the block has the same order of accuracy as the main method. Accuracy of the scheme was tested with numerical examples, the result shows a better performance over the existing schemes. Hence, the new one step method has high order of accuracy with very low error constants. It has large intervals of absolute stability and are zero stable and converges.